National Science Education Standards http://books.nap.edu/html/nses/html/6e.html#csg912

CONTENT STANDARD A: As a result of activities in grades 9-12, all students should develop

• Abilities necessary to do scientific inquiry
• Understandings about scientific inquiry

CONTENT STANDARD B: As a result of their activities in grades 9-12, all students should develop an understanding of

• Motions and forces

CONTENT STANDARD E: As a result of activities in grades 9-12, all students should develop

• Abilities of technological design
• Understandings about science and technology

CONTENT STANDARD F: As a result of activities in grades 9-12, all students should develop understanding of

• Personal and community health
• Population growth
• Natural resources
• Environmental quality
• Natural and human-induced hazards
• Science and technology in local, national, and global challenges

National Council Teachers of Mathematics http://standards.nctm.org/

Algebra

• Use mathematical models to represent and understand quantitative relationships
• Identify essential quantitative relationships in a situation and determine the class or classes of functions that might model the relationships;
• Draw reasonable conclusions about a situation being modeled

Geometry

Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships

• Analyze properties and determine attributes of two- and three-dimensional objects
• Explore relationships (including congruence and similarity) among classes of two- and three-dimensional geometric objects, make and test conjectures about them, and solve problems involving them
• Establish the validity of geometric conjectures using deduction, prove theorems, and critique arguments made by others
• Use trigonometric relationships to determine lengths and angle measures

Use visualization, spatial reasoning, and geometric modeling to solve problems

• Draw and construct representations of two- and three-dimensional geometric objects using a variety of tools;
• Use vertex-edge graphs to model and solve problems;
• Use geometric models to gain insights into, and answer questions in, other areas of mathematics
• Use geometric ideas to solve problems in, and gain insights into, other disciplines and other areas of interest such as art and architecture

Reasoning & Proof

• Recognize reasoning and proof as fundamental aspects of mathematics;
• Make and investigate mathematical conjectures;
• Develop and evaluate mathematical arguments and proofs;
• Select and use various types of reasoning and methods of proof

Problem solving

• Build new mathematical knowledge through problem solving;
• Solve problems that arise in mathematics and in other contexts;
• Apply and adapt a variety of appropriate strategies to solve problems;
• Monitor and reflect on the process of mathematical problem solving.

Communication

• Organize and consolidate their mathematical thinking through communication;
• Communicate their mathematical thinking coherently and clearly to peers, teachers, and others;
• Analyze and evaluate the mathematical thinking and strategies of others;
• Use the language of mathematics to express mathematical ideas precisely.

Connections

• Recognize and use connections among mathematical ideas;
• Understand how mathematical ideas interconnect and build on one another to produce a coherent whole;
• Recognize and apply mathematics in contexts outside of mathematics.

Representation

• Create and use representations to organize, record, and communicate mathematical ideas;
• Select, apply, and translate among mathematical representations to solve problems;
• Use representations to model and interpret physical, social, and mathematical phenomena.

Texas Essential Knowledge and Skills (TEKS) http://www.tea.state.tx.us/teks/

Physicsggg Knowledge and Skills

• Demonstrate safe practices during field and laboratory investigations.
• Plan and implement experimental procedures including asking questions, formulating testable hypotheses, and selecting equipment and technology.
• Make quantitative observations and measurements with precision.
• Organize, analyze, evaluate, make inferences, and predict rends from data.
• Communicate valid conclusions.
• Graph data to observe and identify relationships between variables.
• Evaluate the impact of research on scientific thought, society, and the environment.
• Generate and interpret graphs describing motion including the use of real-time technology.
• Analyze examples of uniform and accelerated motion including linear, projectile, and circular.
• Demonstrate the effects of forces on the motion of objects.

Geometryffff Knowledge and Skills

• Uses constructions to explore attributes of geometric figures and to make conjectures about geometric relationships
• Makes and verifies conjectures about angles, lines, polygons, circles, and three-dimensional figures, choosing from a variety of approaches such as coordinate, transformational, and axiomatic.
• Uses inductive reasoning to formulate a conjecture.
• Uses deductive reasoning to prove a statement.
• Uses numeric and geometric patterns to make generalizations about geometric properties, including properties of polygons, ratios in similar figures and solids, and angle relationships in polygons and circles.
• Uses concrete models based on exploration to test conjectures about the properties of parallel and perpendicular lines.
• Uses concrete models based on exploration to formulate and test conjectures about the properties and attributes of circles and the lines that intersect them.

Precalculusffff Knowledge and Skills

• Use regression to determine a function to model real-life data
• Solve problems from physical situations using trigonometry, including the use of Law of Sines, Law of Cosines, and area formulas.
• Use the concept of vectors to model situations defined by magnitude and direction.

Math Modelsfffff Knowledge and Skills

• Compare and analyze various methods for solving a real-life problem.
• Use multiple approaches (algebraic, graphical, and geometric methods) to solve problems from a variety of disciplines
• Select a method to solve a problem, defend the method, and justify the reasonableness of the results.
• Interpret information from various graphs, including line graphs, bar graphs, circle graphs, histograms, and scatter plots to draw conclusions from the data
• Use regression methods available through technology to describe various models for data such as linear, quadratic, exponential, etc., select the most appropriate model, and use the model to interpret information.
• Formulate a meaningful question, determine the data needed to answer the question, gather the appropriate data, analyze the data, and draw conclusions
• Communicate methods used, analysis conducted, and conclusions drawn for a data-analysis project by written report, visual display, oral report, or multi-media presentation
• Determine the appropriateness of a model for making predictions from a given set of data.
• Use trigonometric ratios and functions available through technology to calculate distances and model periodic motion.